A Class of Indefinite Dogleg Path Methods for Unconstrained Minimization

In this paper we propose a convenient curvilinear search method to solve trust region problems arising from unconstrained optimization problems. The curvilinear paths we set forth are dogleg paths, generated mainly by employing Bunch--Parlett factorization for general symmetric matrices that may be indefinite. This method is easy to implement and globally convergent. It is proved that the method satisfies the first- and second-order stationary point convergence properties and that the convergence rate is quadratic under commonly used conditions on functions. Numerical experiments are conducted to compare this method with some existing methods.